Robust Estimation Method Using Successive Approximation Algorithm to Correct Errors

Robust Estimation Method Using Successive Approximation Algorithm to Correct Errors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Robust Estimation Method Using Successive Approximation Algorithm to Correct Errors Xiao-ming YE This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1212289/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract In measurement practice, the residuals in least squares adjustment usually show various abnormal discrete distributions, including outliers, which is not conducive to the optimization of final measured values. In this paper, according to the physical mechanism of deviation, dispersion and outlier of repeated observations, it can be seen that abnormal distribution and outlier are normal measurement phenomena, and weakening the influence of outlier is an incorrect research direction. Then, by revealing the advantages of functional model processing, this paper puts forward the error correction idea of using the approximate function model to approach the actual function model step by step, and forms a new theoretical method to optimize the final measured values, which greatly improves the quality of measured values. This is a new measurement theory idea that is completely different from mainstream robust estimation research. Applied Mathematics Robust estimation Least square method Gross error Outlier Function model Full Text Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1212289","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":73204028,"identity":"e982b83c-3625-42dd-9f43-5fa2f0c9d7a7","order_by":0,"name":"Xiao-ming YE","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYLCCD2CSB0QwE6eDcQbJWph5SNJicO2M4WObP7V2DRK5xyQYKqwTG9jPHsCrRXJ2jrFxbtvx5AaJvDQJhjPpiQ08eQl4tfBL55hJ5zYcS2YAMiQY2w4nNkjwGODVwiadY/7b4g9Myz8itIBsYWZgq7GDaGkgQovk7LRiyd62Awls8m+MLRKOpRu38eTg12JwO3njhx9/6uz5ec4Y3vhQYy3bz34GvxYGBg6QgsOJbSB2Ash3BNQDAfsDIFFnT1jhKBgFo2AUjFgAAGTtPgrl90AyAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-8227-4181","institution":"Wuhan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Xiao-ming","middleName":"","lastName":"YE","suffix":""}],"badges":[],"createdAt":"2021-12-29 03:07:07","currentVersionCode":2,"declarations":"","doi":"10.21203/rs.3.rs-1212289/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-1212289/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":30635928,"identity":"ee0b41b0-ea09-4f49-b6c8-aa0bd04bae7f","added_by":"auto","created_at":"2022-12-21 16:43:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":347739,"visible":true,"origin":"","legend":"","description":"","filename":"SuccessiveApproximation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1212289/v2/74880accb036d0688831c35c.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eRobust Estimation Method Using Successive Approximation Algorithm to Correct Errors\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Robust estimation, Least square method, Gross error, Outlier, Function model","lastPublishedDoi":"10.21203/rs.3.rs-1212289/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1212289/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn measurement practice, the residuals in least squares adjustment usually show various abnormal discrete distributions, including outliers, which is not conducive to the optimization of final measured values. 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